Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
314 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #64118 | C2 | semidirect |
| 3. #63866 | C2 | semidirect |
| 4. #63831 | C2 | semidirect |
| 5. C3×#825 | C2 | semidirect |
| 6. C3×#824 | C2 | semidirect |
| 7. #63570 | C2 | semidirect |
| 39. #825 | D3 | semidirect |
| 40. #824 | D3 | semidirect |
| 221. C32 | #456 | semidirect |
| 266. C3 | #4752 | semidirect |
| 267. C3 | #4826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64297 | 2 |
| #64118 | 2 |
| #63866 | 2 |
| #63831 | 2 |
| C3×#825 | 2 |
| C3×#824 | 2 |
| #63570 | 2 |
| #4826 | 3 |
| #4752 | 3 |